Three squares are placed as shown. Given that the green areas are equal, what is the side length of the orange square?

## An Italian hill

Two semicircles inside a rectangle. What is the proportion of the red to the green area?

## Domino day

Three congruent rectangles consisting of two squares each are placed as shown. What is the blue area?

## The carambole

Three touching congruent circles inscribed in an equilateral triangle. A small equilateral triangle inscribed in the centre space. What fraction is blue?

## The eye of the beholder

A square and two equilateral triangles inside and touching a circle. What’s the angle α?

## The star of Bethlehem

Two concentric equilateral triangles with parallel sides. What fraction is orange?

## The christmas tree

A triangle, a median and another cevian. What is the proportion of the two areas?

## The bowtie

A square and two congruent isosceles triangles with variable top angle. What is the maximum fraction shaded?

## The inner triangle

A triangle and two medians. What fraction is shaded?

## The ace of diamonds

Four congruent right triangles form a rectangle. What fraction is red?